English

An unoriented skein exact triangle for knot Floer homology

Geometric Topology 2008-02-14 v3 Symplectic Geometry

Abstract

Given a crossing in a planar diagram of a link in the three-sphere, we show that the knot Floer homologies of the link and its two resolutions at that crossing are related by an exact triangle. As a consequence, we deduce that for any quasi-alternating knot, the total rank of its knot Floer homology is equal to the determinant of the knot.

Keywords

Cite

@article{arxiv.math/0609531,
  title  = {An unoriented skein exact triangle for knot Floer homology},
  author = {Ciprian Manolescu},
  journal= {arXiv preprint arXiv:math/0609531},
  year   = {2008}
}

Comments

13 pages, 10 figures; 9_46 dropped from the list of quasi-alternating knots